(CNN) -- Though they support some federal action to help their states recover from the recession, several Republican governors said Sunday they plan to turn down a portion of what's offered in the stimulus bill that President Obama signed last week.

Gov. Haley Barbour said the stimulus bill would force Mississippi to raise taxes.

"If we were to take the unemployment reform package that they have, it would cause us to raise taxes on employment when the money runs out -- and the money will run out in a couple of years," Mississippi Gov. Haley Barbour told CNN's "State of the Union" on Sunday.

The Republican governors of Idaho, Alaska, Texas, South Carolina and Louisiana expressed similar concerns. But one of their colleagues, California Gov. Arnold Schwarzenegger, had a message for them Sunday on ABC's "This Week."

When asked about broader complaints from lawmakers such as South Carolina Gov. Mark Sanford about the stimulus package leading to more debt, Schwarzenegger responded, "I am more than happy to take his money or [that of] any other governor in this country that doesn't want to take this money. I take it because I think California needs it."

Schwarzenegger said he does not foresee a need for a tax hike in the future to sustain the unemployment provisions.

In a separate interview on CNN's "State of the Union," Schwarzenegger said the complaints are "partially" right, but that using the money for now "cannot hurt." And another governor, Michigan Democrat Jennifer Granholm, told CNN, "We'll take it." Watch how stimulus package could affect your paycheck »

"South Carolina, I'll take your money. Louisiana, we'll take it," Granholm said in an interview recorded last week and broadcast Sunday on "State of the Union."

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"We got plenty of work here, plenty of jobs that we would like to create here," Granholm added as she discussed the struggling auto industry and job losses in her state.

A leading Democrat, meanwhile, said he does see a potential problem.

"I'm not sure that we can, over the long run, cope with the high unemployment compensation standard that this mandates for states," Pennsylvania Gov. Ed Rendell, the head of the National Governor's Association, told "Fox News Sunday."

"But I don't care. My people are suffering," he added. "They need that extra money. And right now that's paramount in my mind."

At issue is a portion of the unemployment assistance stipulated by the stimulus bill, which provides federal dollars to expand unemployment insurance in the states. In exchange for accepting that, states would have to expand the number of people who are given jobless benefits.

In Louisiana, for example, that portion of the funds would total nearly $100 million, state officials said. Gov. Bobby Jindal, a rising GOP star, has announced plans to turn it down.

"The $100 million we turned down was temporary federal dollars that would require us to change our unemployment laws," he told NBC's "Meet the Press."

"That would have actually raised taxes on Louisiana businesses. We as a state would have been responsible for paying for those benefits after the federal money disappeared."

The law demands a "permanent" change to state law, Jindal said.

Jindal and the other governors do plan to accept other funds offered by the stimulus, including money to increase benefits for those who are receiving them. And even some governors who have expressed disappointment in the stimulus package are not shying away from any of the funding.

"I don't like this bill, but it is now the law. ... It's now our responsibility and opportunity to try to implement it," Minnesota Gov. Tim Pawlenty told "Fox News Sunday."

Calling his state "a major net subsidizer of the federal government," he said, "We're paying the bill either way -- we're going to take our share of the money."

In the end, some governors who would like to turn down a portion of the federal funding may not be able to. The law stipulates that state legislatures can overrule governors.

Massachusetts Gov. Deval Patrick, a Democrat, said Americans are making it clear to all governors that they should accept whatever help they can get.

"Everywhere across the country, certainly in Massachusetts ... people want their roads repaired, they want their bridges repaired, they want a clean energy strategy ... and real alternatives, and they want us to be candid with them about those needs," he told CNN's "State of the Union."